论文标题
离散马尔可夫添加过程的退出时间
Exit Times for a Discrete Markov Additive Process
论文作者
论文摘要
在本文中，我们考虑（无跳过）离散时间和离散空间马尔可夫添加链（MAC），并为所谓的$ \ tilde {w} $和$ \ tilde {z} $ scale矩阵开发理论。证明在确定许多退出问题和相关波动身份中起着至关重要的作用。在这种完全离散的设置中发展的理论遵循类似的推理行，与马尔可夫添加剂过程中的类似理论相似，并被利用以获得比例矩阵的概率构造，确定生成功能的形式，并产生了$ \ tilde {w} $的简单递归关系，并与其与该群体的群体相连。除了标准的一侧和双面退出问题（向上和向下）外，我们还得出了与一个和两边的“反射”过程相关的许多数量的分布特性。
In this paper we consider (upward skip-free) discrete-time and discrete-space Markov additive chains (MACs) and develop the theory for the so-called $\tilde{W}$ and $\tilde{Z}$ scale matrices. which are shown to play a vital role in the determination of a number of exit problems and related fluctuation identities. The theory developed in this fully discrete setup follows similar lines of reasoning as the analogous theory for Markov additive processes in continuous-time and is exploited to obtain the probabilistic construction of the scale matrices, identify the form of the generating function and produce a simple recursion relation for $\tilde{W}$, as well as its connection with the so-called occupation mass formula. In addition to the standard one and two-sided exit problems (upwards and downwards), we also derive distributional characteristics for a number of quantities related to the one and two-sided `reflected' processes.
